Find the length (in cm) of an arc of a circle with radius 12 cm if the arc subtends a central angle of 30°.
30° = π/6 radians
s = rθ = 12(π/6) = 2π
i think u meant the subject math -_-
21
Find the arc length of a circle with a radius of 12 in and a central angle of 300°.
To find the length of an arc of a circle, you need to use the formula:
Arc Length = (θ/360°) * 2πr
Where:
- θ is the central angle subtended by the arc
- r is the radius of the circle
In this case, θ is 30° and the radius is 12 cm. Now we can substitute these values into the formula and calculate the arc length:
Arc Length = (30°/360°) * 2π * 12 cm
First, divide 30° by 360° to convert it into a decimal fraction:
Arc Length = (30/360) * 2π * 12 cm
Simplifying the fraction gives:
Arc Length = (1/12) * 2π * 12 cm
Now, multiply 1/12 by 2π:
Arc Length = (1/12) * 2 * 3.14 * 12 cm
Calculating this expression gives:
Arc Length = 0.0833 * 6.28 * 12 cm
Simplifying this gives:
Arc Length ≈ 7.539 cm
Therefore, the length of the arc of a circle with radius 12 cm, subtending a central angle of 30°, is approximately 7.539 cm.